Based On The Shanghai Stock Index Nonlinear Features Of Fractal Theory Research

For many researches of capital market problems, such as capital asset pricing,financial risk measure and prevention, the choice of portfolio investment, as well asfinancial derivatives pricing etc, the premise lies on the understanding and descriptionof market’s equilibrious and fluctuant character. The capital market is a non-linear andcomplex system, that nature dooms its behavior traits should be found and analyzeddepending on non-linear theory rather than traditional linear paradigm.Fractal theory is an important component of nonlinear systems theoretics, whosebirth not only made a profound impact that changes the human being’s view of nature,scientific concept, methodology and ways of thinking, but also provided a new tool forfinancial research, even opened up a new horizon. According to a three-level schemeformed from examination, analysis and application, this thesis applies this theory intothe reality of Shanghai stock market. With non-linear statistical tests of index sequence,the original assumption of yield normal distribution is rejected and the existence ofnonlinear structure is proved by BDS test. Then two algorithms, stock data-based andimage-based respectively, are programmed to compute the stock dimension. Thatprovides a practical calculation method for box dimension to describe scale invarianceand complexity feature of stock index. Besides, in the light of the average cycle lengthof Shanghai stock market, sub-section amelioration for the rescaling range analysis ismade to obtain Hurst exponent, which is a very important parameter to indicate thelong-term relevance of nonlinear time series. Finally, combined with recent data,taking12bank stocks in Shanghai market as an example, a revelatory application ofnon-linear characteristic parameters for stock risk identification is discussed.Afterwards, comparing with the real history trend and facts of stock market, aninnovative Hurst index calculation method under rolling cycle window is created andput into demonstration. This method can be seemed as an initial thinking for the marketforecasting and early warning.From fractal theory perspective, the paper roundly probes into the non-linearstructure of Shanghai stock index with some specific unique features in both analysiscomputing and applications. The content and conclusions of this study make greatsignificance in many aspects as breaking out the constraints of traditional theory,understanding and grasping the non-linear characteristics of China’s stock market truly in a scientific way, calculating the non-linear parameters accurately, giving investorsproper decision-making analysis and reasonable proposals. In addition, it also ignitesnew ideas for risk management and trend forecasting. And further more, the researchwill supply influential theoretical reference value for the follow-up optimization andimprovement of a series crucial financial issues.